Constantinescu, Corina D, Ramirez, Jorge M and Zhu, Wei R
(2019)
An application of fractional differential equations to risk theory.
FINANCE AND STOCHASTICS, 23 (4).
pp. 1001-1024.
Text
FDE in risk theory.pdf - Author Accepted Manuscript Download (479kB) | Preview |
Abstract
This paper defines a new class of fractional differential operators alongside a family of random variables whose density functions solve fractional differential equations equipped with these operators. These equations can be further used to construct fractional integro-differential equations for the ruin probabilities in collective renewal risk models, with inter-arrival time distributions from the aforementioned family. Gamma-time risk models and fractional Poisson risk models are two specific cases among them, whose ruin probabilities have explicit solutions, when claim sizes distributions exhibit rational Laplace transforms.
Item Type: | Article |
---|---|
Uncontrolled Keywords: | Ruin probability, Fractional differential operator, Collective risk model |
Depositing User: | Symplectic Admin |
Date Deposited: | 04 Jun 2019 15:27 |
Last Modified: | 19 Jan 2023 00:41 |
DOI: | 10.1007/s00780-019-00400-8 |
Open Access URL: | https://link.springer.com/article/10.1007/s11009-0... |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3044391 |